Polymeric liquids dilute

In most cases polymer solutions are not ideally dilute. In fact they exhibit pronounced intermolecular interactions. First approaches dealing with this phenomenon date back to Bueche [35]. Proceeding from the fundamental work of Debye [36] he was able to show that below a critical molar mass Mw the zero-shear viscosity is directly proportional to Mw whereas above this critical value r 0 is found to be proportional to (Mw3,4) [37,38]. This enhanced drag has been attributed to intermolecular couplings. Ferry and co-workers [39] reported that the dynamic behaviour of polymeric liquids is strongly influenced by coupling points. 

The brief data presented in this chapter concerning the initial steps of structure formation in LC polymer solutions, are significant from two viewpoints. On the one hand, the study of these processes provides quantitative information about the molecular parameters and IMM of LC polymers, which is the basis for the understanding and prediction of physico-chemical behaviour of polymeric liquid crystals in bulk. On the other hand, understanding of the features of intramolecular structure formation in dilute solution, reveals broad prospects for the investigation of the formation of lyotropic LC systems of polymers with mesogenic side groups, which is in its infancy 195). 

The Rouse model is the earliest and simplest molecular model that predicts a nontrivial distribution of polymer relaxation times. As described below, real polymeric liquids do in fact show many relaxation modes. However, in most polymer liquids, the relaxation modes observed do not correspond very well to the mode distribution predicted by the Rouse theory. For polymer solutions that are dilute, there are hydrodynamic interactions that affect the viscoelastic properties of the solution and that are unaccounted for in the Rouse theory. These are discussed below in Section 3.6.1.2. In most concentrated solutions or melts, entanglements between long polymer molecules greatly slow polymer relaxation, and, again, this is not accounted for in the Rouse theory. Reptation theories for entangled... 

Figure 6.17 Normalized intrinsic viscosity [r ]/[)7]o for a dilute solution of poly(y-benzyl-L-glutamate) (PBLG) = 208,000) in m-cresol. The line is a calculation for the rigid-dumbbell model, with the relaxation time t = lj6Dro adjusted to the value 10- sec to obtain a fit. The stress tensor for a suspension of rigid dumbbells is given by Eq. (6-36) with Cstr replaced by k T/Dro-(From Bird et al. 1987 data from Yang 1958, Dynamics of Polymeric Liquids, VoL 2, Copyright 1987. Reprinted by permission of John Wiley Sons, Inc.)...

We can see that Eqs. (2 101) (2-104) are sufficient to calculate the continuum-level stress a given the strain-rate and vorticity tensors E and SI. As such, this is a complete constitutive model for the dilute solution/suspension. The rheological properties predicted for steady and time-dependent linear flows of the type (2-99), with T = I t), have been studied quite thoroughly (see, e g., Larson34). Of course, we should note that the contribution of the particles/macromolecules to the stress is actually quite small. Because the solution/suspension is assumed to be dilute, the volume fraction is very small, (p 1. Nevertheless, the qualitative nature of the particle contribution to the stress is found to be quite similar to that measured (at larger concentrations) for many polymeric liquids and other complex fluids. For example, the apparent viscosity in a simple shear flow is found to shear thin (i.e., to decrease with increase of shear rate). These qualitative similarities are indicative of the generic nature of viscoelasticity in a variety of complex fluids. So far as we are aware, however, the full model has not been used for flow predictions in a fluid mechanics context. This is because the model is too complex, even for this simplest of viscoelastic fluids. The primary problem is that calculation of the stress requires solution of the full two-dimensional (2D) convection-diffusion equation, (2-102), at each point in the flow domain where we want to know the stress. 

What do we mean by a polymeric fluid It is a viscous liquid, made of heavily entangled polymer chains. In particular, it could be a polymer melt, a concentrated or a semi-dilute polymer solution. You can easily get a feel for what these are like. All you need to do is melt a piece of ordinary plastic, so that it starts flowing. Obviously the most significant reason why polymeric liquids are important is because they are encountered in all technological processes of plastic production. Polymeric fluids are quite peculiar. In many ways, they are nothing like water or any other ordinary fluid that we are used to. 

The KSR and Rouse models were subj ected to numerous experimental tests. A reasonably good agreement between the theoretical predictions and experimental data was demonstrated for a variety of dilute polymeric solutions. Further advance in the molecular-kinetic approach to description of relaxation processes in polymeric systems have brought about more sophisticated models. They improve the classical results by taking into account additional factors and/or considering diverse frequency, temperature, and concentration ranges, etc. For the aims of computer simulation of the polymeric liquid dynamics in hydrodynamic problems, either simple approximations of the spectrum, Fi(A), or the model of subchains are usually used. Spriggs law is the most used approximation... 

The influence of non-linearity of diffusional transport is higher for diluted solutions. This is explained by a decrease in the deviation of the surface concentration, k, from the bulk ko with lowering ko. This takes place due to simultaneous increase in 0T/3k that is characteristic of polymeric liquids. The presence of a nearly horizontal domain on the curve... 

Experimental investigations of heat transfer at boiling of polymeric liquids cover highly diluted (c = 15 to 500 ppm), low-concentrated (c 1%), and concentrated solutions (c>10%). The data represent diversity of physical mechanisms that reveal themselves in boiling processes. The relative contribution of different physical factors can vary significantly with changes in concentration, temperature, external conditions, etc., even for polymers of the same type and approximately equal molecular mass. For dilute solutions this is clearly demonstrated by the experimentally detected both intensification of heat transfer at nucleate boiling and the opposite effect, viz. a decrease in the heat removal rate in comparison with a pure solvent. 

Figure 7.2.15. The average bubble detachment diameter in boiling dilute aqueous solutions of PEG. AT = 15K. For curves 1-3 the flow velocity v = 0, 5x10, and lO" m/s, respectively. [Adapted, from S.P. Levitsky, and Z.P. Shulman, Bubbles in polymeric liquids, Technomic Publish. Co., Lancaster, 1995, with permission from Technomic Publishing Co., Inc., copyright 1995]...

In some cases, solvents do remain in the final product One sueh example oeeurs in the preparation of liquid vanillin composition used in food and cosmetics production. The preparation of such a solution is complex. The solution must be pourable at room temperature, have high solids concentration (50-70%), be mechanically and chemically stable, be easy to dilute, be transparent, be stable to bacteria, and inexpensive. The solvents include water, ethanol, and propylene glycol. Polymeric liquid crystals are prepared by dispersing polysaccharide in water. These liquid crystals arc used for perfumes. Xanthan gum is also in use for thickening cosmetics. ... 

The relaxation time (A), which describes the time required for the polymer coil to relax from a deformed state back to its equilibrium configuration, is a key parameter for characterizing a viscoelastic fluid. For a fluid with large A, the stresses relax slowly and the elastic effects can be observed even at low deformation rates. A fluid with small A can also exhibit significant elastic effects provided that the deformation rate is high. Clearly, both the fluid characteristic time (the relaxation time) and the flow characteristic time (e.g., the inverse of the deformation rate) are crucial in determining the viscoelastic response of a viscoelastic liquid. For many polymeric liquids, X lies between 10 s for dilute solutions and 10 s for concentrated solutions. 

Phosphoryl triamide, PO(NH2)3, can be made by the direct reaction of liquid ammonia with phosphoryl chloride (7.48), or with triphenyl phosphate (7.64). It forms colourless needles which are very soluble in water, but insoluble in most organic solvents. Prolonged heating results in transformation into polymeric material. Dilute acid hydrolysis or atmospheric moisture will yield mono-ammonium phosphoramidate, while with dilute NaOH, sodium phosphorodiamidate is formed (7.65)... 

Let us look at typical behavior of these material functions. In Figure 3.3.5 we see that G versus o) looks similar to G versus 1/r from Figure 3.3.1. For rubber it becomes constant at low frequency (long times), and for concentrated polymeric liquids it shows the plateau modulus Ge and decreases with co in the limit of low frequency. The loss modulus is much lower than G for a crosslinked rubber and sometimes can show a local maximum. This maximum is more pronounced in polymeric liquids, especially for narrow molecular weight distribution. The same features are present in dilute suspensions of rodlike particles, but not for dilute random coil polymer solutions, as Figure 3.3.3b shows. These applications of the dynamic moduli to structural characterization are discussed in Chapters 10 and 11. 

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